Subdivisions of oriented cycles in digraphs with large chromatic number
Subdivisions of oriented cycles in digraphs with large chromatic number
An oriented cycle is an orientation of a undirected cycle. We first show that for any oriented cycle $C$, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number. In contrast, we show that for any $C$ a cycle with two blocks, every strongly …